Design: Blocked RCT, with 3 levels, and randomization done at level 1 (individual level).

Models: random treatment effects.

  • M = 3
  • J = 30
  • K = 15
  • \(\bar{n} = 100\) (unless otherwise noted)
  • rho: \(\rho\) = 0.5
  • ATE ES = 0.125, 0.125, 0.125
  • R2: \(R^2_1\) = 0.1, 0.1, 0.1, \(R^2_2\) = 0.1, 0.1, 0.1, \(R^2_3\) = 0.1, 0.1, 0.1
  • ICC: \(\text{ICC}_2\) = 0.2, 0.2, 0.2, \(\text{ICC}_3\) = 0.2, 0.2, 0.2
  • Omega: \(\omega_2\) = 0.1, \(\omega_3\) = 0.1

Power Validation

Base case

Varying school size

\(\bar{n}\) = 75

\(\bar{n}\) = 50

Varying R2

\(R^2_1 =\) 0.6, 0.6, 0.6

\(R^2_2 =\) 0.6, 0.6, 0.6

\(R^2_3 =\) 0.6, 0.6, 0.6

\(R^2_1 =\) 0, 0, 0 \(R^2_2 =\) 0, 0, 0 \(R^2_3 =\) 0, 0, 0

Varying rho

\(\rho =\) 0.2

\(\rho =\) 0.8

Varying true positives

ATE (ES) = 0.125, 0, 0

Varying ICC

\(\text{ICC}_2\) = 0.7, 0.7, 0.7

\(\text{ICC}_3\) = 0.7, 0.7, 0.7

\(\text{ICC}_2\) = 0, 0, 0

\(\text{ICC}_2\) = 0.2, 0.2, 0.2

Varying Omega

\(\omega_2\) = 0.8, \(\omega_3\) = 0.1

\(\omega_2\) = 0.1, \(\omega_3\) = 0.8

\(\omega_2\) = 0.8, \(\omega_3\) = 0.8

\(\omega_2\) = 0, \(\omega_3\) = 0.1

\(\omega_2\) = 0.1, \(\omega_3\) = 0

\(\omega_2\) = 0, \(\omega_3\) = 0

Kappa

\(\kappa\) = 0.4

MDES validation

## 
## 
## +------------+---------------+---------------+-------------+
## |    MTP     | Adjusted MDES | D1indiv Power | Target MDES |
## +============+===============+===============+=============+
## |    rawp    |     0.102     |     0.704     |    0.125    |
## +------------+---------------+---------------+-------------+
## | Bonferroni |     0.124     |     0.704     |    0.125    |
## +------------+---------------+---------------+-------------+
## |     BH     |     0.124     |     0.834     |    0.125    |
## +------------+---------------+---------------+-------------+
## |    Holm    |     0.126     |     0.808     |    0.125    |
## +------------+---------------+---------------+-------------+
## 
## Table: d3.1_m3rr2rr

Sample size validation

## 
## 
## +------+-------------+-------------+---------------+
## | MTP  | Sample type | Sample size | D1indiv power |
## +======+=============+=============+===============+
## |  BH  |      J      |     30      |     0.834     |
## +------+-------------+-------------+---------------+
## | Holm |      J      |     NA      |      NA       |
## +------+-------------+-------------+---------------+
## 
## Table: d3.1_m3rr2rr
## 
## 
## +------+-------------+-------------+---------------+
## | MTP  | Sample type | Sample size | D1indiv power |
## +======+=============+=============+===============+
## |  BH  |      K      |     15      |     0.831     |
## +------+-------------+-------------+---------------+
## | Holm |      K      |     15      |     0.794     |
## +------+-------------+-------------+---------------+
## 
## Table: d3.1_m3rr2rr
## 
## 
## +------+-------------+-------------+---------------+
## | MTP  | Sample type | Sample size | D1indiv power |
## +======+=============+=============+===============+
## |  BH  |    nbar     |     77      |     0.83      |
## +------+-------------+-------------+---------------+
## | Holm |    nbar     |     NA      |      NA       |
## +------+-------------+-------------+---------------+
## 
## Table: d3.1_m3rr2rr